6-loop anomalous dimension of a single impurity operator from AdS/CFT and multiple zeta values

Anomalous dimension of the simplest nontrivial single impurity operator in the beta=1/2 deformed theory is determined at six loops from the AdS/CFT correspondence. L\"uscher correction is evaluated at next-to-next-to-leading order (NNLO) in terms of multiple zeta values. The result can be simplified into the products of simple zeta functions and the same form of the correction is expected for the Konishi operator at six loops, too.Comment: 14 pages, references added, numeric coefficient in (5) corrected, which changes the numerical result, but not its structur

Discrete physical states and correction terms in the Supersymmetric c=1 Model of String Theory

In this work, we explore the example of supersymmetric c=1 model which is one of the simplest models of superstrings, with an elegant and transparent spectrum of physical states. We show how the presence of the ghost cohomologies enlarges the spectrum of states and leads to new intriguing symmetries of the theory and possibly leads to nontrivial relations of two-dimensional supergravity with physical theories in higher dimensions. We develop a general prescription for constructing the BRST-invariant and nontrivial vertex operators and we explicitly compute correction terms that restore BRST invariance of their corresponding currents.Comment: 15 pages. arXiv admin note: substantial text overlap with arXiv:hep-th/0602209, arXiv:hep-th/0701044 by other author

The Dynamics of COVID-19 spread: Evidence from Lebanon

We explore the spread of the Coronavirus disease 2019 (COVID-19) in Lebanon by adopting two different approaches: the STEIR model, which is a modified SEIR model accounting for the effect of travel, and a repeated iterations model. We fit available daily data since the first diagnosed case until the end of June 2020 and we forecast possible scenarios of contagion associated with different levels of social distancing measures and travel inflows. We determine the initial reproductive transmission rate in Lebanon and all subsequent dynamics. In the repeated iterations (RI) model we iterate the available data of currently infected people to forecast future infections under several possible scenarios of contagion. In both models, our results suggest that tougher mitigation measures would slow down the spread of the disease. On the other hand, the current relaxation of measures and partial resumption of international flights, as the STEIR reveals, would trigger a second outbreak of infections, with severity depending on the extent of relaxation. We recommend strong institutional and public commitment to mitigation measures to avoid uncontrolled spread.Comment: The final preprint of the published paper that covers data from February 21 until July 1, 2020 and incorporates travel effects. 15 pages, 7 figure

Fruitless (fru) and the Neural System of Rejection Behaviours in Female Drosophila melanogaster

Among sexually reproducing organisms, species are separated by their inability to reproduce with each other and form viable, fertile offspring. One type of reproductive barrier is behavioural, whereby mating is not initiated between two species. In the model organism Drosophila melanogaster, a gene called fruitless regulates heterospecific courtship and rejection behaviours, however, its neural mechanisms of action remain unknown in females. In this work, I identified which fruitless splice variants are expressed in adult males and females, and created the plasmid vectors necessary to implement a genetic system for the purposes of identifying, silencing, and hyperactivating neuronal subsets that express distinct splice-variants of fruitless. These plasmid vectors can be used in the future to induce expression of exogenous genes of interest for further experimentation in D. melanogaster

Finite-Volume Spectra of the Lee-Yang Model

We consider the non-unitary Lee-Yang minimal model ${\cal M}(2,5)$ in three different finite geometries: (i) on the interval with integrable boundary conditions labelled by the Kac labels $(r,s)=(1,1),(1,2)$, (ii) on the circle with periodic boundary conditions and (iii) on the periodic circle including an integrable purely transmitting defect. We apply $\varphi_{1,3}$ integrable perturbations on the boundary and on the defect and describe the flow of the spectrum. Adding a $\Phi_{1,3}$ integrable perturbation to move off-criticality in the bulk, we determine the finite size spectrum of the massive scattering theory in the three geometries via Thermodynamic Bethe Ansatz (TBA) equations. We derive these integral equations for all excitations by solving, in the continuum scaling limit, the TBA functional equations satisfied by the transfer matrices of the associated $A_{4}$ RSOS lattice model of Forrester and Baxter in Regime III. The excitations are classified in terms of $(m,n)$ systems. The excited state TBA equations agree with the previously conjectured equations in the boundary and periodic cases. In the defect case, new TBA equations confirm previously conjectured transmission factors.Comment: LateX, 42 pages with 22 eps figure